Roughly speaking, it's because the waves are emitted from the region outside the black holes, being created by the in-spiraling of two black holds before/during

Roughly speaking, it's because the waves are emitted from the region outside the black holes, being created by the in-spiraling of two black holds before/during their merger. Once the black holes merge and settle down, they stop emitting gravitational waves. But that's just a cartoon. Strictly speaking, the picture of a wave traveling with respect to a fixed background spacetime is only an accurate approximation when the wave is very weak. In the immediate neighborhood of a black hole merger, the approximation breaks down, and you just have to look how the whole spacetime itself is evolving (usually through simulation).